In　this　paper,　we　propose　an　optimal　entanglement　concentration　protocol　(ECP)　for　partially　entangled　cluster　states　with　the　help　of　the　weak　cross-Kerr　nonlinearity.　We　can　obtain　the　maximally　entangled　cluster　states　assisted　with　the　projection　measurements　on　the　additional　photons.　The　protocol　is　based　on　optical　elements,　single　polarization　photons,　cross-Kerr　nonlinearity,　and　the　conventional　photon　detectors,　which　are　feasible　with　existing　experimental　technology.　Numerical　simulation　demonstrates　that　by　iterating　the　entanglement　concentration　process　n=m=6　times,　the　ECP　has　the　approximate　maximal　success　probability　100 %.　Moreover,　the　present　protocol　is　also　suitable　for　partially　entangled　4N-photon　cluster　states　concentration.　All　these　advantages　make　this　protocol　more　efficient　and　more　convenient　than　others　in　the　applications　in　quantum　communication.　©　2015,　Springer　Science+Business　Media　New　York.